Differential Equations

Let y = y(x) be the solution of the differential equation \({{dy} \over {dx}} = 1 + x{e^{y - x}}, - \sqrt 2 < x < \sqrt 2 ,y(0) = 0\)

then, the minimum value of \(y(x),x \in \left( { - \sqrt 2 ,\sqrt 2 } \right)\) is equal to :